Scheduling model and resource pricing in multi-stage manufacturing systems

The scheduling model of multi-stage manufacturing systems with multiple job classes and variable production capacity constraints at workstations was built to make the total cost minimum. On the basis of analyzing optimal conditions, the prices of production capacities or resources were derived and explained in economic meaning. It has been shown that the dynamic scheduling model can be transformed into the equivalent static minimum cost flow problem over space-time extended network. The modified Frank-Wolfe algorithm was used to solve the equivalent problem. The illustrative example was given.